As a promising distributed technology, federated learning (FL) has been widely used in vehicular networks involving large amounts of IoT-enabled sensor data, which derives federated vehicular networks (FVNs). However, the efficiency of FVN is generally limited by vehicle selection policy and communication conditions, which leads to high communication costs and latency. The original FVN transmits model parameters from a random subset of vehicles to the roadside unit (RSU) and ignores the diversity of learning quality among vehicles. In addition, a few vehicles with poor wireless channel conditions may prolong communication latency. To address these two issues, we propose a communication-efficient federated learning approach, composed of Vehicle Selection, Student–Project Allocation (SPA) matching model, and Convex Optimization, called FedSSC, to improve the communication efficiency in FVN. The parameter variations for the same vehicle in two consecutive rounds are used to quantify the quality of the learning results by cosine distance and Affinity Propagation (AP) clustering. Moreover, a subchannel allocation algorithm based on the SPA matching model, as well as a convex optimal power allocation solution are integrated to minimize the communication latency of each training round. According to extensive experiments, the proposed FedSSC reduces the communication overhead by 26.32% on average compared with the benchmarks, whereas the communication latency decreases by 21.84%.